{"id":"https://openalex.org/W2216621377","doi":"https://doi.org/10.1007/978-3-662-43414-7_6","title":"A Group Action on $${\\mathbb Z}_p^{\\times }$$ and the Generalized DLP with Auxiliary Inputs","display_name":"A Group Action on $${\\mathbb Z}_p^{\\times }$$ and the Generalized DLP with Auxiliary Inputs","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2216621377","doi":"https://doi.org/10.1007/978-3-662-43414-7_6","mag":"2216621377"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-662-43414-7_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-43414-7_6","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044011121","display_name":"Jung Hee Cheon","orcid":"https://orcid.org/0000-0002-7085-2220"},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]},{"id":"https://openalex.org/I4210158432","display_name":"National Institute for Mathematical Sciences","ror":"https://ror.org/04n7py080","country_code":"KR","type":"education","lineage":["https://openalex.org/I4210158432"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Jung Hee Cheon","raw_affiliation_strings":["Department of Mathematical Sciences and ISaC-RIM, Seoul National University, Seoul, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences and ISaC-RIM, Seoul National University, Seoul, South Korea","institution_ids":["https://openalex.org/I4210158432","https://openalex.org/I139264467"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067172615","display_name":"Tae-Chan Kim","orcid":"https://orcid.org/0000-0003-1683-8484"},"institutions":[{"id":"https://openalex.org/I4210158432","display_name":"National Institute for Mathematical Sciences","ror":"https://ror.org/04n7py080","country_code":"KR","type":"education","lineage":["https://openalex.org/I4210158432"]},{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Taechan Kim","raw_affiliation_strings":["Department of Mathematical Sciences and ISaC-RIM, Seoul National University, Seoul, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences and ISaC-RIM, Seoul National University, Seoul, South Korea","institution_ids":["https://openalex.org/I4210158432","https://openalex.org/I139264467"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036960562","display_name":"Yongsoo Song","orcid":"https://orcid.org/0000-0002-0496-9789"},"institutions":[{"id":"https://openalex.org/I139264467","display_name":"Seoul National University","ror":"https://ror.org/04h9pn542","country_code":"KR","type":"education","lineage":["https://openalex.org/I139264467"]},{"id":"https://openalex.org/I4210158432","display_name":"National Institute for Mathematical Sciences","ror":"https://ror.org/04n7py080","country_code":"KR","type":"education","lineage":["https://openalex.org/I4210158432"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Yong Soo Song","raw_affiliation_strings":["Department of Mathematical Sciences and ISaC-RIM, Seoul National University, Seoul, South Korea"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences and ISaC-RIM, Seoul National University, Seoul, South Korea","institution_ids":["https://openalex.org/I4210158432","https://openalex.org/I139264467"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5044011121"],"corresponding_institution_ids":["https://openalex.org/I139264467","https://openalex.org/I4210158432"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.3624,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.64410494,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"121","last_page":"135"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.7138580083847046},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6884604096412659},{"id":"https://openalex.org/keywords/discrete-logarithm","display_name":"Discrete logarithm","score":0.6589393615722656},{"id":"https://openalex.org/keywords/greatest-common-divisor","display_name":"Greatest common divisor","score":0.6330609321594238},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6215720772743225},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.5760473608970642},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5478730201721191},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5382435321807861},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.4795224964618683},{"id":"https://openalex.org/keywords/multiplicative-group","display_name":"Multiplicative group","score":0.4736531972885132},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.44410985708236694},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.4413042962551117},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43581968545913696},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4292380213737488},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33361899852752686},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18427947163581848},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16373658180236816},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.1455221176147461}],"concepts":[{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.7138580083847046},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6884604096412659},{"id":"https://openalex.org/C173259116","wikidata":"https://www.wikidata.org/wiki/Q864003","display_name":"Discrete logarithm","level":4,"score":0.6589393615722656},{"id":"https://openalex.org/C125257309","wikidata":"https://www.wikidata.org/wiki/Q131752","display_name":"Greatest common divisor","level":2,"score":0.6330609321594238},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6215720772743225},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.5760473608970642},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5478730201721191},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5382435321807861},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.4795224964618683},{"id":"https://openalex.org/C92788228","wikidata":"https://www.wikidata.org/wiki/Q3777923","display_name":"Multiplicative group","level":3,"score":0.4736531972885132},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.44410985708236694},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.4413042962551117},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43581968545913696},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4292380213737488},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33361899852752686},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18427947163581848},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16373658180236816},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.1455221176147461},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.0},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-662-43414-7_6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-662-43414-7_6","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1491251281","https://openalex.org/W1523567567","https://openalex.org/W1660562555","https://openalex.org/W1905774212","https://openalex.org/W1963716248","https://openalex.org/W1985592521","https://openalex.org/W2014239329","https://openalex.org/W2057636642","https://openalex.org/W2116556172","https://openalex.org/W2117685508","https://openalex.org/W2117797270","https://openalex.org/W2152924492","https://openalex.org/W2160580401","https://openalex.org/W2170293373","https://openalex.org/W2172174332","https://openalex.org/W2401035169","https://openalex.org/W2402461229","https://openalex.org/W2612543848","https://openalex.org/W2970789867","https://openalex.org/W3030649634","https://openalex.org/W3030850646","https://openalex.org/W4252614677","https://openalex.org/W4285719527","https://openalex.org/W4289127653"],"related_works":["https://openalex.org/W4380051813","https://openalex.org/W2046780104","https://openalex.org/W2171286238","https://openalex.org/W4221139454","https://openalex.org/W2062309499","https://openalex.org/W2283856749","https://openalex.org/W1975216581","https://openalex.org/W2258462132","https://openalex.org/W1983651862","https://openalex.org/W2246898167"],"abstract_inverted_index":null,"counts_by_year":[{"year":2020,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}